Calculation of hydrogenic form factors

Abstract

An algorithm is presented for evaluating transition matrix elements between hydrogenic or hydrogen-like partial waves for arbitrary multiple orders. In general, the result can be represented by a sum of Appell's F2 functions of two variables (1926), which reduces to a polynomial when at least one of the states is bound. To illustrate the method and study the convergence in partial waves, the authors present calculations of the total cross section for electron impact ionisation of atomic hydrogen.